Creating time varying 2d coordinates with OrnsteinUhlenbeckProcess

Question

I see that I can create time varying 1d data with e.g.

SeedRandom[1]; 

mu = 0.3; 
sigma = 0.5; 
theta = 0.4; 

ntimes = 1000; 
x = RandomFunction[
       OrnsteinUhlenbeckProcess[mu, sigma, theta], {1/ntimes, 1, 1/ntimes}
    ];

time = Range@ntimes; xt = Transpose[{time, x[[2, 1, 1]]}]; 

ListLinePlot[xt, ImageSize -> Medium, Frame -> True, FrameLabel -> {"time", "x"}]

How can I create 2d coordinates (data) that are varying with time using OrnsteinUhlenbeckProcess?

To plot the 2d trajectory I would use:

ListLinePlot[data, ImageSize -> Medium, Frame -> True, 
   FrameLabel -> {"y", "x"}, AspectRatio -> Automatic]

Answer 1

I think I found a solution. I would be happy if somebody could verify it.

SeedRandom[1];

mu = 0.3; 
sigma = 0.5; 
theta = 0.4;

ntimes = 1000;

xy = RandomFunction[
      OrnsteinUhlenbeckProcess[mu, sigma, theta], {1/ntimes, 1, 1/ntimes}, 2][[2]];

data = Transpose[{xy[[1, 1, All]], xy[[1, 2, All]]}];

ListLinePlot[data, ImageSize -> Medium, Frame -> True, 
  FrameLabel -> {"x", "y"}, AspectRatio -> Automatic]